axiom-source 20170501-3 / usr / share / axiom-20170501 / src / algebra / ODVAR.spad

)abbrev domain ODVAR OrderlyDifferentialVariable
++ Author:  William Sit
++ Date Created: 19 July 1990
++ Date Last Updated: 13 September 1991
++ References:Kolchin, E.R. "Differential Algebra and Algebraic Groups"
++   (Academic Press, 1973).
++ Description:
++ \spadtype{OrderlyDifferentialVariable} adds a commonly used orderly
++ ranking to the set of derivatives of an ordered list of differential
++ indeterminates.  An orderly ranking is a ranking \spadfun{<} of the
++ derivatives with the property that for two derivatives u and v,
++ u \spadfun{<} v if the \spadfun{order} of u is less than that of v.
++ This domain belongs to \spadtype{DifferentialVariableCategory}.  It
++ defines \spadfun{weight} to be just \spadfun{order}, and it
++ defines an orderly ranking \spadfun{<} on derivatives u via the
++ lexicographic order on the pair
++ (\spadfun{order}(u), \spadfun{variable}(u)).

OrderlyDifferentialVariable(S) : SIG == CODE where
  S : OrderedSet

  SIG ==> DifferentialVariableCategory(S)

  CODE ==> add

    Rep := Record(var:S, ord:NonNegativeInteger)

    makeVariable(s,n) == [s, n]

    variable v     == v.var

    order v        == v.ord